Word Problems Leading to Quadratic Equations

🧠 Quiz: 3.6 Word Problems Leading to Quadratic Equations

1. The product of two consecutive integers is 56. What is the equation?

\(x(x+1) = 56\) \(x^2 + 56 = 0\) \(x(x-1) = 56\) \(x^2 - 56 = 0\)

2. The area of a square is 144. What quadratic equation represents its side length?

\(x^2 = 120\) \(x^2 - 144 = 0\) \(x^2 + 144 = 0\) \(x^2 - 12 = 0\)

3. A rectangle has length \(x\) and width \(x-3\). If area = 70, what equation arises?

\(x(x-3) = 70\) \(x^2 - 70 = 0\) \(x^2 + 3x - 70 = 0\) \(x^2 - 3x - 64 = 0\)

4. The sum of squares of two consecutive integers is 85. What equation forms?

\(x^2 + (x+1)^2 = 85\) \(x^2 + (x-2)^2 = 85\) \(x^2 - (x+1)^2 = 85\) \(x^2 + 85 = 0\)

5. A number added to its reciprocal equals 10. What equation results?

\(x + \frac{1}{x} = 10\) \(x^2 + 1 = 10x\) \(x^2 - 10x + 1 = 0\) All of the above

6. The perimeter of a square is 48. What quadratic equation gives its area?

\(4x = 48\) \(x = 12\) \(x^2 = 124\) \(x^2 - 144 = 0\)

7. The sum of a number and its square is 72. What equation arises?

\(x + x^2 = 72\) \(x^2 + x - 72 = 0\) Both a and b None

8. The difference of squares of two consecutive integers is 15. What equation?

\((x+1)^2 - x^2 = 15\) \(2x+1 = 15\) \(x = 7\) All of the above

9. A number is 2 less than its square. What equation represents this?

\(x^2 - x - 2 = 0\) \(x^2 + x - 2 = 0\) \(x^2 - 2x - 1 = 0\) \(x^2 - 2 = 0\)

10. The sum of a number and its square is equal to 30. What quadratic equation arises?

\(x + x^2 = 30\) \(x^2 + x - 30 = 0\) Both a and b None